USP: an independence test that improves on Pearson's chi-squared and the G-test.

We present the U -statistic permutation (USP) test of independence in the context of discrete data displayed in a contingency table. Either Pearson's χ 2 -test of independence, or the G -test, are typically used for this task, but we argue that these tests have serious deficiencies, both in terms of their inability to control the size of the test, and their power properties. By contrast, the USP test is guaranteed to control the size of the test at the nominal level for all sample sizes, has no issues with small (or zero) cell counts, and is able to detect distributions that violate independence in only a minimal way. The test statistic is derived from a U -statistic estimator of a natural population measure of dependence, and we prove that this is the unique minimum variance unbiased estimator of this population quantity. The practical utility of the USP test is demonstrated on both simulated data, where its power can be dramatically greater than those of Pearson's test, the G -test and Fisher's exact test, and on real data. The USP test is implemented in the R package USP.

Vascular Positron Emission Tomography and Restenosis in Symptomatic Peripheral Arterial Disease: A Prospective Clinical Study.

OBJECTIVES: This study determined whether in vivo positron emission tomography (PET) of arterial inflammation (18F-fluorodeoxyglucose [18F-FDG]) or microcalcification (18F-sodium fluoride [18F-NaF]) could predict restenosis following PTA. BACKGROUND: Restenosis following lower limb percutaneous transluminal angioplasty (PTA) is common, unpredictable, and challenging to treat. Currently, it is impossible to predict which patient will suffer from restenosis following angioplasty. METHODS: In this prospective observational cohort study, 50 patients with symptomatic peripheral arterial disease underwent 18F-FDG and 18F-NaF PET/computed tomography (CT) imaging of the superficial femoral artery before and 6 weeks after angioplasty. The primary outcome was arterial restenosis at 12 months. RESULTS: Forty subjects completed the study protocol with 14 patients (35%) reaching the primary outcome of restenosis. The baseline activities of femoral arterial inflammation (18F-FDG tissue-to-background ratio [TBR] 2.43 [interquartile range (IQR): 2.29 to 2.61] vs. 1.63 [IQR: 1.52 to 1.78]; p < 0.001) and microcalcification (18F-NaF TBR 2.61 [IQR: 2.50 to 2.77] vs. 1.69 [IQR: 1.54 to 1.77]; p < 0.001) were higher in patients who developed restenosis. The predictive value of both 18F-FDG (cut-off TBRmax value of 1.98) and 18F-NaF (cut-off TBRmax value of 2.11) uptake demonstrated excellent discrimination in predicting 1-year restenosis (Kaplan Meier estimator, log-rank p < 0.001). CONCLUSIONS: Baseline and persistent femoral arterial inflammation and micro-calcification are associated with restenosis following lower limb PTA. For the first time, we describe a method of identifying complex metabolically active plaques and patients at risk of restenosis that has the potential to select patients for intervention and to serve as a biomarker to test novel interventions to prevent restenosis.

Site and Burden of Lower Limb Atherosclerosis Predicts Long-term Mortality in a Cohort of Patients With Peripheral Arterial Disease.

OBJECTIVE/BACKGROUND: Lower limb peripheral arterial disease (PAD) is becoming increasingly common. Lower limb perfusion, as determined by the ankle brachial pressure index (ABPI), is a recognised predictor of overall mortality. The increasing role of non-invasive imaging in patient assessment may aid in the ability to predict poor patient outcomes. METHODS: This study included all patients undergoing a lower limb arterial duplex over a period of 20 months. The site and burden of atherosclerosis within the lower limb was determined using the well validated Bollinger score. Patient demographic data were also collated. The primary outcome measure was all cause mortality. RESULTS: A total of 678 patients were included (median age 74 years). The overall median follow up period was 69.9 months. Of these, 307 patients reached the primary end point, which was death. Independent predictors of all cause mortality included total Bollinger score (odds ratio [OR] 1.11, 95% confidence interval [CI] 1.05-1.18 [p < .001]; OR per 10 points), femoropopliteal Bollinger score (OR 1.34, 95% CI 1.11-1.08 [p = .05]; OR per 10 points), and crural Bollinger score (OR 1.03, 95% CI 1.01-1.03 [p = .03]). There was also a significant association between mortality and age, a prior history of ischaemic heart disease, a history of congestive cardiac failure and chronic renal failure (chronic kidney disease ≥ 3). Statin and antiplatelet therapy were protective. CONCLUSION: This contemporary study confirms poor long-term outcomes still exist in patients with PAD. The site and severity of lower limb atherosclerosis are independent predictors of long-term mortality.